1. Field of the Invention
The present invention relates to an error correcting apparatus for digital data and a digital synchronizing detecting apparatus.
2. Description of the Prior Art
It is customary that, when a digital information is transmitted, an error that takes place in a transmission line is detected and then corrected.
According to the coding theory, a fundamental theory for error correction lies in that a Hamming distance between code words (symbol sequences) is large.
Of pairs of symbols located on two symbol sequences u and v of the same length at their corresponding positions, the number of different pairs is called a Hamming distance of symbol sequences u and v. The Hamming distance is expressed as d.sub.H (u, v). The Hamming distance will sometimes be referred to as simply a distance in the description which follows.
In a block code in which lengths of all code words are finite and equal, a minimum value of Hamming distance between different code words is called a minimum (Hamming) distance. This minimum (Hamming) distance is expressed as d.sub.min.
As shown in FIG. 1 of the accompanying drawings, sets of symbol sequences each having a distance less than t from code words c.sub.i, c.sub.j are conceptually expressed by circles having a radius t and centers c.sub.i and c.sub.j, respectively. The above sets have no common portion when the following condition is established: EQU d.sub.min .gtoreq.2t+1
If e (.ltoreq.t) errors occur in a transmission line when the code word c.sub.i of the block code is transmitted and a code word r is received, then e is expressed as: EQU e=d.sub.H (c.sub.i, r).ltoreq.t
At that time, the following condition is established for an arbitrary code word c.sub.j other than the code word c.sub.i. EQU d.sub.H (c.sub.i, r)&lt;t
If it is determined that a code word x that satisfies d.sub.H (x, r).ltoreq.t is transmitted for the received word r, then error less than t errors (t-fold) can be corrected thoroughly.
Code words whose d.sub.min is more than 2t.sub.2 +1 can correct errors of t.sub.1 fold and can detect errors of t.sub.1 and t.sub.2 fold.
In conventional magnetic recording of a digital signal, taking electro-magnetic characteristics into consideration, original data are converted into proper modulation codes such as 8-10 converted modulation code, 8-14 modulation code or the like, having at least less DC component and less consecutive bits of the same polarity, and then are recorded.
Usually, in the modulation code, according to a predetermined modulation rule (rule), sample data corresponding to all input data sequences are stored in a ROM (read only memory) as a table.
If incorrect sample data, which are not included in the ROM table, are obtained departing from the modulation rule due to errors mainly occurring in the electro-magnetic system upon playback, then on the basis of all samples in the ROM table, the Hamming distances between them and the reference sample are calculated by the comparison of incorrect samples with the reference samples in a one-to-one fashion. The incorrect sample is decoded to a sample whose Hamming distance is closest to the reference sample. That is, the error is corrected according to the minimum distance decoding method.
In the magnetic recording of the digital signal, the distance between code words is generally short due to the restrictions concerning the modulation code as described before. There is then the problem that a satisfactory error correction capability cannot be always obtained according to the conventional minimum distance decoding method.
As shown in FIG. 2 of the accompanying drawings, if incorrect sample data e.sub.1, e.sub.2, e.sub.3 are obtained outside a modulation code space Rc, then the incorrect sample data e.sub.1 includes a code word c.sub.2 which has the minimum distance within the modulation code space Rc so that the error can be corrected.
The incorrect sample e.sub.2, however, includes two minimum distance code words c.sub.4, c.sub.5 within the space Rc so that the error cannot be corrected by the minimum distance decoding method.
Let it now be assumed that upon playback a sample Spb="011001001" is obtained in the magnetic recording and reproducing system that employs the 3-9 modulation shown on the following table 1.
In the sample Spb, only #2 bit is different from a first row reference sample Sr0="011001101" corresponding to an original signal "0" on the table 1 and only #3 bit is different from a reference sample Sr1="011100001" corresponding to a second row original signal "1".
In this case, the reproduced sample Spb has the Hamming distance [1] between it and both the reference samples Sr0, Sr1. Therefore, the reproduced sample Spb cannot specify the closest sample and can only detect the error.
TABLE 1 ______________________________________ INTER- ORIGI- MEDIATE NAL DATA 3-9 MODULATION CODE SIGNAL (NRZ) #8 7 6 5 4 3 2 1 0 ______________________________________ 0 0 0 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 1 2 0 1 0 0 1 1 1 0 0 0 0 1 3 0 1 1 0 1 0 0 0 0 0 1 1 4 1 0 0 0 1 1 1 1 0 0 0 1 5 1 0 1 0 0 1 1 1 0 0 0 1 6 1 1 0 0 0 0 0 1 1 1 1 1 7 1 1 1 0 0 0 1 1 0 0 0 1 ______________________________________
When the digital information is transmitted, a synchronizing (sync.) signal of a predetermined pattern is inserted into a digital information DATA at a proper cycle following a pre-amble PA, as shown in FIG. 3 of the accompanying drawings.
As the above sync. signal, there is selected a sync. signal of a pattern whose Hamming distance for all digital modulation codes is large. For the modulation codes shown on the following table 2, the following sync. pattern Csy is selected so as to have a Hamming distance of 2 or more.
Csy="00111110"
TABLE 2 __________________________________________________________________________ DISTANCE ORIGINAL INTERMEDIATE MODULATION CODE TO SYNC. SIGNAL DATA #7 6 5 4 3 2 1 0 PATTERN __________________________________________________________________________ 0 0 0 0 0 1 1 0 0 1 1 3 1 0 1 0 1 1 0 0 1 1 1 5 2 1 0 0 0 0 1 1 1 0 0 2 3 1 1 0 0 1 1 0 0 0 1 4 __________________________________________________________________________
As is conventional, the sync. pattern is not error-corrected due to the following reason:
A special pattern having a large Hamming distance for all digital modulation codes is selected as the sync. pattern as described before so that, if the error in the sync. pattern is corrected, the Hamming distance of the sync. pattern for the digital modulation code is reduced and the error correction becomes meaningless.
There is then the problem that the probability that an error will occur in the sync. pattern itself is increased.
Further, if the error in the sync. pattern is forcibly corrected, then the smaller the Hamming distance relative to the digital modulation code becomes, the more the number of patterns which are regarded as the sync. pattern is increased. There is then the problem that the probability that the modulation code will be changed to the sync. pattern due to the occurrence of error is increased, i.e., the probability that the pseudo-sync. signal will occur is increased.
When the distance between an error pattern to be corrected and the modulation code is short, the probability that the pseudo-sync. signal will occur tends to be deteriorated.
If the above sync. pattern Csy is changed as shown on the following table 3 due to one-bit error, then a third row error pattern Cec="00011110" corresponding to "C" on the table 3 is different only in #1 bit from a modulation code Cm2="00011100" corresponding to the original signal "2" on the table 2. Further, a seventh row error pattern Ceg="00111100" corresponding to "g" on the table 3 is different only in #5 bit from the modulation code Cm2 corresponding to "2" on the table 2.
TABLE 3 ______________________________________ ERROR ERROR PATTERN NUMBER #7 6 5 4 3 2 1 0 ______________________________________ a 1 0 1 1 1 1 1 0 b 0 1 1 1 1 1 1 0 c 0 0 0 1 1 1 1 0 d 0 0 1 0 1 1 1 0 e 0 0 1 1 0 1 1 0 f 0 0 1 1 1 0 1 0 g 0 0 1 1 1 1 0 0 h 0 0 1 1 1 1 1 1 ______________________________________
As conceptually shown in FIG. 4 of the accompanying drawings, a Hamming distance between the error patterns Cec, Ceg within one-bit error space Re1 and the modulation code Cm2 within the modulation code space Rc becomes [1]. It is natural that the one-bit error patterns Cec, Ceg have a Hamming distance [1] between them and the sync. pattern Csy.
Accordingly, each of the error patterns Cec, Ceg has the equal distance between it and the sync. pattern Csy and the modulation code Cm2 and equal to them in probability so that the error patterns Cec, Ceg cannot be corrected. If the error patterns Cec, Ceg are forcibly corrected, then the probability that the pseudo-sync. signal will occur is deteriorated.